(February 4, 2022 at 10:35 am)Fireball Wrote: Why "257"? Were the lower versions already used?
It is a Fermat prime. There are only 5 such known: 3, 5, 17, 257, 65537.
And yes, 3, 5, and 17 tend to be taken.
Fermat primes have a very deep connection with which polygons can be constructed by straightedge and compass as well as other aspects of algebraic number theory.